Description :- Elementary geometrical solids refer to the basic three dimensional shapes that form the foundation of geometry. These solids have defined properties, including the number of faces, edges, and vertices. Here’s an overview of some of the most common elementary geometrical solids: 1. Cube  Faces: 6 square faces  Edges: 12 edges  Vertices: 8 vertices  Properties: All edges are equal in length, and the angles between faces are all 90 degrees. A cube is a special case of a rectangular prism where all sides are equal. 2. Cuboid (Rectangular Prism)  Faces: 6 rectangular faces  Edges: 12 edges  Vertices: 8 vertices  Properties: Opposite faces are equal, and all angles are 90 degrees. A cuboid can have varying lengths, widths, and heights. 3. Sphere  Faces: 1 curved surface (no edges or vertices)  Edges: None  Vertices: None  Properties: All points on the surface are equidistant from the center, and it has perfect symmetry in all directions. 4. Cylinder  Faces: 2 circular faces and 1 curved lateral surface  Edges: 2 edges (where the circular faces meet the lateral surface)  Vertices: None  Properties: A cylinder has circular symmetry around its axis and a fixed height. The two circular faces are congruent, and the lateral surface is curved. 5. Cone  Faces: 1 circular base and 1 curved lateral surface

 Edges: 1 edge (the circumference of the base)  Vertices: 1 vertex (the apex)  Properties: A cone has a circular base and tapers to a single point (the apex). The lateral surface is curved, connecting the base to the apex. 6. Pyramid  Faces: 1 polygonal base and triangular faces that meet at a common vertex (the apex)  Edges: The number of edges depends on the base polygon; for a square pyramid, it has 8 edges.  Vertices: The number of vertices depends on the base polygon; for a square pyramid, it has 5 vertices (4 at the base and 1 at the apex).  Properties: A pyramid has a polygonal base and triangular faces that converge to a point (apex). The number of faces and edges increases with the number of sides on the base. 7. Tetrahedron  Faces: 4 triangular faces  Edges: 6 edges  Vertices: 4 vertices  Properties: A tetrahedron is a type of pyramid with a triangular base. It is a regular polyhedron, meaning all its faces and edges are congruent. 8. Octahedron  Faces: 8 triangular faces  Edges: 12 edges  Vertices: 6 vertices  Properties: An octahedron is a regular polyhedron with 8 equilateral triangular faces. It can be seen as two pyramids joined at their bases. 9. Dodecahedron  Faces: 12 regular pentagonal faces  Edges: 30 edges  Vertices: 20 vertices  Properties: A dodecahedron is a regular polyhedron with 12 faces, each a regular pentagon. It has a more complex symmetry than the tetrahedron or cube. 10. Icosahedron  Faces: 20 equilateral triangular faces  Edges: 30 edges

 Vertices: 12 vertices  Properties: An icosahedron is another regular polyhedron with 20 faces, all of which are equilateral triangles. These elementary solids can be classified into two categories:  Platonic Solids: These are convex polyhedra with identical faces composed of regular polygons. There are five Platonic solids: tetrahedron, cube, octahedron, dodecahedron, and icosahedron.  Other Solids: These include shapes like the sphere, cylinder, cone, and pyramid, which may not fit the strict definition of polyhedra but are still fundamental in geometry. Each of these shapes has unique properties, making them crucial in various fields such as architecture, physics, engineering, and art.